Charm mixing tests the Standard Model

A report from the LHCb experiment

The Standard Model (SM) allows neutral flavoured mesons such as the D⁰ to oscillate into their antiparticles. Having first observed this process in 2012, the LHCb collaboration has recently made some of the world’s most precise measurements of this behaviour, which is potentially sensitive to new physics. The oscillation of the D⁰ (cu̅) into its antiparticle, the D̅⁰ (c̅u), occurs through the exchange of massive virtual particles. These might include as-yet undiscovered particles, so the measurements are sensitive to non-Standard Model dynamics at large energy scales. By examining D⁰ and D̅⁰ mesons separately, it is also possible to search for the violation of charge–parity (CP) symmetry in the charm sector. Such effects are predicted to be very small. Therefore, given LHCb’s current level of experimental precision, any sign of CP violation would be a clear indication of physics beyond the Standard Model.

Given LHCb’s current level of experimental precision, any sign of CP violation would be a clear indication of physics beyond the Standard Model.

Due to quantum-mechanical mixing between the neutral charm meson’s mass and flavour eigenstates, the probabilities of observing either it or its antiparticle vary as a function of time. This mixing can be described by two parameters, x and y, which relate the properties of the mass eigenstates: x is the normalised difference in mass, and y is the normalised difference in width, or inverse lifetime. The mixing rate is very slow, making these parameters difficult to measure. Isolating the differences between the D⁰ and D̅⁰ mesons is an even greater challenge. For these two papers, LHCb was able to achieve small statistical uncertainties thanks to the large samples of charm mesons collected during Run 1, and minimised systematic uncertainties by measuring ratios of yields to cancel detector effects.

In the first paper, LHCb physicists studied the effective lifetime of the mesons. As a consequence of mixing, the effective decay width to CP-even final states, such as K⁺K^– and π⁺π^–, differs from the average width measured in decays such as D⁰ → K^– π⁺. The parameter y_CP, which in the limit of CP symmetry is equal to y, can be deduced from the ratio of decay rates to these two final states as a function of time. LHCb measured y_CP with the same precision as all previous measurements combined, obtaining a value consistent with the world-average value of y.

In the second analysis, LHCb reconstructed D⁰ decays into the final state K⁰_Sπ⁺π^– to measure the parameter x, which had not previously been shown to differ from zero. In this mode, mixing manifests as small variations in the decay rate in different parts of phase space as a function of time. Measuring it requires good control over experimental effects as a function of both phase space and decay time. LHCb achieved this by measuring the ratios of the yields in complementary regions of phase space (mirrored in the Dalitz plane) as a function of time. The measured value of x is the world’s most precise, and in combination with previous measurements there is now evidence that it differs from zero.

As well as the mixing itself, both analyses are also sensitive to mixing-induced CP violation. While CP violation was not observed, the limits on its parameters were greatly improved (figure 1). This is a good example of how different decay modes give complementary information and, when taken together, can have a big impact. LHCb will continue to perform measurements with additional modes and the larger samples collected in Run 2.